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Simplifying 4x2 + 15x + -236 = 0 Reorder the terms: -236 + 15x + 4x2 = 0 Solving -236 + 15x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -59 + 3.75x + x2 = 0 Move the constant term to the right: Add '59' to each side of the equation. -59 + 3.75x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + 3.75x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + 3.75x + x2 = 0 + 59 3.75x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 3.75x + x2 = 59 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 59 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 59 + 3.515625 Combine like terms: 59 + 3.515625 = 62.515625 3.515625 + 3.75x + x2 = 62.515625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 62.515625 Calculate the square root of the right side: 7.9066823 Break this problem into two subproblems by setting (x + 1.875) equal to 7.9066823 and -7.9066823.Subproblem 1
x + 1.875 = 7.9066823 Simplifying x + 1.875 = 7.9066823 Reorder the terms: 1.875 + x = 7.9066823 Solving 1.875 + x = 7.9066823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 7.9066823 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 7.9066823 + -1.875 x = 7.9066823 + -1.875 Combine like terms: 7.9066823 + -1.875 = 6.0316823 x = 6.0316823 Simplifying x = 6.0316823Subproblem 2
x + 1.875 = -7.9066823 Simplifying x + 1.875 = -7.9066823 Reorder the terms: 1.875 + x = -7.9066823 Solving 1.875 + x = -7.9066823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -7.9066823 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -7.9066823 + -1.875 x = -7.9066823 + -1.875 Combine like terms: -7.9066823 + -1.875 = -9.7816823 x = -9.7816823 Simplifying x = -9.7816823Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.0316823, -9.7816823}
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